Mean, Median, Mode and Range -- Sorted Sets (Sets of 5 from 10 to ... - Free Printable

To solve the problem, we need to calculate the mean, median, mode, and range for each set of numbers. Let's go through each step systematically.

Definitions:

1. Mean: The average of the numbers. It is calculated as:
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of elements}}
\]

2. Median: The middle number when the numbers are arranged in ascending order. If there is an even number of elements, the median is the average of the two middle numbers.

3. Mode: The number that appears most frequently in the set. If no number repeats, there is no mode.

4. Range: The difference between the largest and smallest numbers in the set:
\[
\text{Range} = \text{Largest number} - \text{Smallest number}
\]

Step-by-Step Solution:

#### 1. \(\{18, 18, 63, 84\}\)
- Mean:
\[
\text{Mean} = \frac{18 + 18 + 63 + 84}{4} = \frac{183}{4} = 45.75
\]
- Median: Arrange in ascending order: \(18, 18, 63, 84\). The median is the average of the two middle numbers:
\[
\text{Median} = \frac{18 + 63}{2} = \frac{81}{2} = 40.5
\]
- Mode: The number that appears most frequently is \(18\).
- Range:
\[
\text{Range} = 84 - 18 = 66
\]

#### 2. \(\{19, 21, 29, 32, 89\}\)
- Mean:
\[
\text{Mean} = \frac{19 + 21 + 29 + 32 + 89}{5} = \frac{190}{5} = 38
\]
- Median: Arrange in ascending order: \(19, 21, 29, 32, 89\). The median is the middle number:
\[
\text{Median} = 29
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 89 - 19 = 70
\]

#### 3. \(\{41, 41, 41, 44, 90\}\)
- Mean:
\[
\text{Mean} = \frac{41 + 41 + 41 + 44 + 90}{5} = \frac{257}{5} = 51.4
\]
- Median: Arrange in ascending order: \(41, 41, 41, 44, 90\). The median is the middle number:
\[
\text{Median} = 41
\]
- Mode: The number that appears most frequently is \(41\).
- Range:
\[
\text{Range} = 90 - 41 = 49
\]

#### 4. \(\{25, 37, 39, 85, 85\}\)
- Mean:
\[
\text{Mean} = \frac{25 + 37 + 39 + 85 + 85}{5} = \frac{271}{5} = 54.2
\]
- Median: Arrange in ascending order: \(25, 37, 39, 85, 85\). The median is the middle number:
\[
\text{Median} = 39
\]
- Mode: The number that appears most frequently is \(85\).
- Range:
\[
\text{Range} = 85 - 25 = 60
\]

#### 5. \(\{12, 36, 64, 65, 82\}\)
- Mean:
\[
\text{Mean} = \frac{12 + 36 + 64 + 65 + 82}{5} = \frac{259}{5} = 51.8
\]
- Median: Arrange in ascending order: \(12, 36, 64, 65, 82\). The median is the middle number:
\[
\text{Median} = 64
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 82 - 12 = 70
\]

#### 6. \(\{30, 57, 59, 76, 91\}\)
- Mean:
\[
\text{Mean} = \frac{30 + 57 + 59 + 76 + 91}{5} = \frac{313}{5} = 62.6
\]
- Median: Arrange in ascending order: \(30, 57, 59, 76, 91\). The median is the middle number:
\[
\text{Median} = 59
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 91 - 30 = 61
\]

#### 7. \(\{27, 27, 49, 77, 84\}\)
- Mean:
\[
\text{Mean} = \frac{27 + 27 + 49 + 77 + 84}{5} = \frac{264}{5} = 52.8
\]
- Median: Arrange in ascending order: \(27, 27, 49, 77, 84\). The median is the middle number:
\[
\text{Median} = 49
\]
- Mode: The number that appears most frequently is \(27\).
- Range:
\[
\text{Range} = 84 - 27 = 57
\]

#### 8. \(\{25, 46, 62, 76, 97\}\)
- Mean:
\[
\text{Mean} = \frac{25 + 46 + 62 + 76 + 97}{5} = \frac{306}{5} = 61.2
\]
- Median: Arrange in ascending order: \(25, 46, 62, 76, 97\). The median is the middle number:
\[
\text{Median} = 62
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 97 - 25 = 72
\]

#### 9. \(\{22, 35, 58, 63, 75\}\)
- Mean:
\[
\text{Mean} = \frac{22 + 35 + 58 + 63 + 75}{5} = \frac{253}{5} = 50.6
\]
- Median: Arrange in ascending order: \(22, 35, 58, 63, 75\). The median is the middle number:
\[
\text{Median} = 58
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 75 - 22 = 53
\]

#### 10. \(\{45, 45, 47, 88, 89\}\)
- Mean:
\[
\text{Mean} = \frac{45 + 45 + 47 + 88 + 89}{5} = \frac{314}{5} = 62.8
\]
- Median: Arrange in ascending order: \(45, 45, 47, 88, 89\). The median is the middle number:
\[
\text{Median} = 47
\]
- Mode: The number that appears most frequently is \(45\).
- Range:
\[
\text{Range} = 89 - 45 = 44
\]

#### 11. \(\{58, 84, 90, 90, 97\}\)
- Mean:
\[
\text{Mean} = \frac{58 + 84 + 90 + 90 + 97}{5} = \frac{419}{5} = 83.8
\]
- Median: Arrange in ascending order: \(58, 84, 90, 90, 97\). The median is the middle number:
\[
\text{Median} = 90
\]
- Mode: The number that appears most frequently is \(90\).
- Range:
\[
\text{Range} = 97 - 58 = 39
\]

#### 12. \(\{25, 36, 36, 40, 68\}\)
- Mean:
\[
\text{Mean} = \frac{25 + 36 + 36 + 40 + 68}{5} = \frac{205}{5} = 41
\]
- Median: Arrange in ascending order: \(25, 36, 36, 40, 68\). The median is the middle number:
\[
\text{Median} = 36
\]
- Mode: The number that appears most frequently is \(36\).
- Range:
\[
\text{Range} = 68 - 25 = 43
\]

#### 13. \(\{18, 18, 33, 34, 54\}\)
- Mean:
\[
\text{Mean} = \frac{18 + 18 + 33 + 34 + 54}{5} = \frac{157}{5} = 31.4
\]
- Median: Arrange in ascending order: \(18, 18, 33, 34, 54\). The median is the middle number:
\[
\text{Median} = 33
\]
- Mode: The number that appears most frequently is \(18\).
- Range:
\[
\text{Range} = 54 - 18 = 36
\]

#### 14. \(\{19, 19, 27, 36, 64\}\)
- Mean:
\[
\text{Mean} = \frac{19 + 19 + 27 + 36 + 64}{5} = \frac{165}{5} = 33
\]
- Median: Arrange in ascending order: \(19, 19, 27, 36, 64\). The median is the middle number:
\[
\text{Median} = 27
\]
- Mode: The number that appears most frequently is \(19\).
- Range:
\[
\text{Range} = 64 - 19 = 45
\]

#### 15. \(\{34, 52, 75, 85, 90\}\)
- Mean:
\[
\text{Mean} = \frac{34 + 52 + 75 + 85 + 90}{5} = \frac{336}{5} = 67.2
\]
- Median: Arrange in ascending order: \(34, 52, 75, 85, 90\). The median is the middle number:
\[
\text{Median} = 75
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 90 - 34 = 56
\]

#### 16. \(\{55, 57, 68, 82, 99\}\)
- Mean:
\[
\text{Mean} = \frac{55 + 57 + 68 + 82 + 99}{5} = \frac{361}{5} = 72.2
\]
- Median: Arrange in ascending order: \(55, 57, 68, 82, 99\). The median is the middle number:
\[
\text{Median} = 68
\]
- Mode: No number repeats, so there is no mode.
- Range:
\[
\text{Range} = 99 - 55 = 44
\]

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{Mean: } 45.75, \text{Median: } 40.5, \text{Mode: } 18, \text{Range: } 66 \\
2. & \text{Mean: } 38, \text{Median: } 29, \text{Mode: } \text{None}, \text{Range: } 70 \\
3. & \text{Mean: } 51.4, \text{Median: } 41, \text{Mode: } 41, \text{Range: } 49 \\
4. & \text{Mean: } 54.2, \text{Median: } 39, \text{Mode: } 85, \text{Range: } 60 \\
5. & \text{Mean: } 51.8, \text{Median: } 64, \text{Mode: } \text{None}, \text{Range: } 70 \\
6. & \text{Mean: } 62.6, \text{Median: } 59, \text{Mode: } \text{None}, \text{Range: } 61 \\
7. & \text{Mean: } 52.8, \text{Median: } 49, \text{Mode: } 27, \text{Range: } 57 \\
8. & \text{Mean: } 61.2, \text{Median: } 62, \text{Mode: } \text{None}, \text{Range: } 72 \\
9. & \text{Mean: } 50.6, \text{Median: } 58, \text{Mode: } \text{None}, \text{Range: } 53 \\
10. & \text{Mean: } 62.8, \text{Median: } 47, \text{Mode: } 45, \text{Range: } 44 \\
11. & \text{Mean: } 83.8, \text{Median: } 90, \text{Mode: } 90, \text{Range: } 39 \\
12. & \text{Mean: } 41, \text{Median: } 36, \text{Mode: } 36, \text{Range: } 43 \\
13. & \text{Mean: } 31.4, \text{Median: } 33, \text{Mode: } 18, \text{Range: } 36 \\
14. & \text{Mean: } 33, \text{Median: } 27, \text{Mode: } 19, \text{Range: } 45 \\
15. & \text{Mean: } 67.2, \text{Median: } 75, \text{Mode: } \text{None}, \text{Range: } 56 \\
16. & \text{Mean: } 72.2, \text{Median: } 68, \text{Mode: } \text{None}, \text{Range: } 44 \\
\end{array}
}
\]